Production methods of gas turbine

ABSTRACT

An object is to reduce the compressor flow rate in comparison with the reference model while maintaining a compression ratio equivalent to that in the reference model. Annulus areas required of a compressor 38 of a derivative gas turbine 200 are determined based on a compressor flow rate and a compression ratio required of the compressor 38 of the derivative gas turbine 200. Under the condition that the annulus area of each stage of the compressor 38 becomes equal to the determined annulus area, an inner radius increment and an outer radius decrement of an initial stage 36a are determined, the inner radius increment and the outer radius decrement of each of intermediate stages 36b-36e are determined so that the inner radius increment is not more than the inner radius increment of the previous stage and the outer radius decrement is not less than the outer radius decrement of the previous stage, and the inner radius increment and the outer radius decrement of a final stage 36f are determined so that the outer radius decrement is not less than the inner radius increment. The compressor 38 is designed by updating design data of components of the reference compressor 15 that deviated from the specifications due to the determination of the inner radius increment and the outer radius decrement so that the updated design data fulfill the specifications in each of the stages 36a-36f.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to design and production methods of a gasturbine.

2. Description of the Related Art

In recent years, new types of turbines such as humid air turbinesinjecting moisture into the intake air of the compressor and blastfurnace gas firing gas turbines using low-calorie blast furnace gas asthe fuel are emerging as derivative models of gas turbines. In caseswhere a derivative model is designed or produced based on a standardtype of gas turbine that uses lamp oil, light oil, natural gas or thelike as the fuel with no humidification of the intake air (referencemodel) at a low cost, it is desirable to reuse as many components of thereference model (i.e., divert as many components from the referencemodel) as possible and thereby reduce the number of components newlydeveloped.

Meanwhile, if the compressor flow rate in a humid air turbine or a blastfurnace gas firing gas turbine is made equal to that in the referencemodel, the turbine flow rate increases in comparison with the referencemodel. Specifically, since the humid air gas turbine supplies moistureto the downstream side of the compressor, the turbine flow rateincreases correspondingly in comparison with the reference model. Alsoin the blast furnace gas firing gas turbine, due to the use of blastfurnace gas as low-calorie fuel, a greater amount of fuel is necessarycompared to cases where a common type of gas turbine fuel (natural gas,petroleum, etc.) is used, and consequently, the turbine flow rateincreases correspondingly in comparison with the reference model.Therefore, in humid air turbines and blast furnace gas firing gasturbines, the turbine has to be newly designed and it is impossible tosimply reuse components of the reference model.

To deal with this problem, there has been proposed a method that reducesthe outer radius of the compressor channel to decrease the annulus areaof the compressor channel, thereby reduces the compressor flow rate, andthereby makes the turbine flow rate equivalent to that in the referencemodel (see U.S. Pat. No. 7,937,947, for example).

SUMMARY OF THE INVENTION

In the method described in U.S. Pat. No. 7,937,947, the length of eachrotor blade in the blade length direction decreases corresponding to thedecrease in the outer radius of the compressor channel. Thus, thecircumferential velocity of each rotor blade decreases and thecompression ratio (pressure ratio) can drop compared to that in thereference model.

The object of the present invention, which has been made inconsideration of the above-described situation, is to provide design andproduction methods of a gas turbine capable of reducing the compressorflow rate in comparison with the reference model while maintaining acompression ratio equivalent to that in the reference model.

To achieve the above object, the present invention provides a gasturbine production method for producing a derivative gas turbine of adifferent cycle based on a reference gas turbine including a referencecompressor. Letting a reference inner radius and a reference outerradius respectively represent an inner radius and an outer radius of anannular compressor channel of the reference compressor, an inner radiusincrement represent an increment in an inner radius of a compressorchannel of the derivative gas turbine with respect to the referenceinner radius, and an outer radius decrement represent a decrement in anouter radius of the compressor channel of the derivative gas turbinewith respect to the reference outer radius, the gas turbine productionmethod includes the steps of: determining a compressor flow rate and acompression ratio required of a compressor of the derivative gasturbine; determining annulus areas required of the compressor of thederivative gas turbine based on the determined compressor flow rate andcompression ratio; determining the inner radius increment and the outerradius decrement of an initial stage, determining the inner radiusincrement and the outer radius decrement of each of intermediate stageson the downstream side of the initial stage so that the inner radiusincrement is not more than the inner radius increment of the previousstage and the outer radius decrement is not less than the outer radiusdecrement of the previous stage, and determining the inner radiusincrement and the outer radius decrement of a final stage on thedownstream side of the intermediate stages so that the outer radiusdecrement is not less than the inner radius increment under a conditionthat the annulus area of each stage of the compressor of the derivativegas turbine becomes equal to the determined annulus area; designing thecompressor of the derivative gas turbine by updating design data ofcomponents of the reference compressor that deviated from specificationsdue to the determination of the inner radius increment and the outerradius decrement so that the updated design data fulfill thespecifications in the initial stage, in each of the intermediate stages,and in the final stage; and producing the compressor of the derivativegas turbine based on the design and thereby producing the derivative gasturbine.

According to the present invention, it is possible to provide design andproduction methods of a gas turbine capable of reducing the compressorflow rate in comparison with the reference model while maintaining acompression ratio equivalent to that in the reference model.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a reference model according to a firstembodiment of the present invention.

FIG. 2 is a schematic diagram of a humid air gas turbine according tothe first embodiment of the present invention.

FIG. 3 is a schematic diagram showing the overall configuration of aconfiguration example of a reference compressor according to the firstembodiment of the present invention.

FIG. 4 is a cross-sectional view taken in the arrow direction of theline IV-IV in FIG. 3.

FIG. 5 is a schematic diagram illustrating the flow of air flowingdownstream through a compressor channel.

FIG. 6 is a flow chart showing a design/production procedure of acompressor according to the first embodiment of the present invention.

FIG. 7 is a schematic diagram for explaining tip cut.

FIG. 8 is a schematic diagram for explaining hub up.

FIG. 9 is a diagram illustrating the relationship between a stageloading factor and blade stages.

FIG. 10 is a diagram illustrating the relationship between a bladeheight decrease ratio and the blade stages.

FIG. 11 is a diagram illustrating compression ratio dependence ofcompressor efficiency.

FIG. 12 is a schematic diagram showing the overall configuration of aconfiguration example of a reference compressor according to a secondembodiment of the present invention.

FIG. 13 is a schematic diagram showing the overall configuration of aconfiguration example of a reference compressor according to a thirdembodiment of the present invention.

FIG. 14 is a schematic diagram showing a configuration example of inletguide vanes according to a fourth embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

First Embodiment

Configuration

1. Reference Model

First, a reference model (reference gas turbine) will be explainedbelow. The reference model in this embodiment is a model (gas turbine)that has past records of design or production and has been selected aswill be explained later.

FIG. 1 is a schematic diagram of the reference model. As shown in FIG.1, the reference model 100 includes a compressor (reference compressor)15, a combustor 16, and a turbine 17.

The reference compressor 15 generates high-pressure compressed air 20 bycompressing air 19 taken in via an air intake part (unshown) andsupplies the compressed air 20 to the combustor 16. The combustor 16causes combustion by mixing fuel with the compressed air 20 obtainedfrom the reference compressor 15, thereby generates high-temperaturecombustion gas 21, and supplies the high-temperature combustion gas 21to the turbine 17. The turbine 17 is driven by the expansion of thecombustion gas 21 obtained from the combustor 16. The referencecompressor 15 is driven by power obtained by the turbine 17, while agenerator 18 is driven by remaining power and generates electric power.The combustion gas 21 after driving the turbine 17 is discharged fromthe turbine 17 as exhaust gas 22. In this embodiment, the referencecompressor 15, the turbine 17 and the generator 18 are interlinked by ashaft 35.

2. Derivative Model

A derivative model (derivative gas turbine) will be explained below bytaking a humid air gas turbine as an example.

FIG. 2 is a schematic diagram of a humid air gas turbine. Parts in FIG.2 equivalent to those of the reference model 100 shown in FIG. 1 areassigned the same reference characters as in FIG. 1 and repeatedexplanation thereof is omitted properly. As shown in FIG. 2, the humidair gas turbine 200 includes a water atomization cooling system 23, ahumidification tower 24, a recuperator 25, and a water recovery system26 in addition to the components of the reference model 100.

The water atomization cooling system 23 generates humid air 27 byspraying water into the air 19 taken in via the air intake part andsupplies the humid air 27 to a compressor 38. The compressor 38generates compressed air 28 by compressing the humid air 27 into whichwater has been sprayed by the water atomization cooling system 23. Theentire flow of the compressed air 28 generated by the compressor 38 isextracted through a gas path outlet of the compressor 38 and is suppliedto the humidification tower 24.

The humidification tower 24 generates humid air 29 by humidifying thecompressed air 28 obtained from the compressor 38 and supplies the humidair 29 to the recuperator 25.

The recuperator 25 heats up the humid air 29 humidified by thehumidification tower 24 by means of heat exchange with exhaust gas 32supplied from the turbine 17 and supplies the heated humid air to thecombustor 16.

The combustor 16 causes combustion by mixing fuel with the humid air 30heated by the recuperator 25, thereby generates high-temperaturecombustion gas 31, and supplies the high-temperature combustion gas 31to the turbine 17. The turbine 17 is driven by the expansion of thecombustion gas 31 obtained from the combustor 16. The combustion gas 31after driving the turbine 17 is supplied to the recuperator 25 as theexhaust gas 32. The exhaust gas 32 supplied to the recuperator 25undergoes heat recovery by means of heat exchange with the exhaust gas29 and is supplied to the water recovery system 26 as exhaust gas 33.

The water recovery system 26 recovers water by cooling down the exhaustgas 33 which has passed through the recuperator 25 and condensingmoisture in the cooled exhaust gas 33. The water recovered by the waterrecovery system 26 is supplied to the humidification tower 24. Theexhaust gas 33 after undergoing the water recovery by the water recoverysystem 26 is discharged from the water recovery system 26 as exhaust gas34.

The humid air gas turbine 200 is capable of recovering thermal energy ofthe exhaust gas 32 by use of the recuperator 25 in order to heat up thehumid air 29. Therefore, assuming that the flow rate of the humid air 27supplied to the compressor 38 (compressor flow rate) is equivalent tothat in the reference model 100, the humid air gas turbine 200 iscapable of reducing the flow rate of the fuel supplied to the combustor16 in comparison with the reference model 100 and thereby increasing theefficiency of the gas turbine cycle. Further, the humid air gas turbine200 is capable of increasing the turbine flow rate and the turbineoutput power by adding moisture to the compressed air 28 in thehumidification tower 24. Furthermore, the humid air gas turbine 200 iscapable of increasing the efficiency of the gas turbine cycle since theamount of thermal energy recovered by the recuperator 25 can beincreased by increasing the flow rate of the humid air 29 while loweringits temperature through the addition of moisture to the compressed air28 in the humidification tower 24.

3. Production of Derivative Model

In the humid air gas turbine 200, the turbine flow rate increasescompared to that in the reference model 100, and thus the turbine has tobe newly designed and it is impossible to simply reuse the turbine 17 ofthe reference model 100. In this embodiment, the humid air gas turbine200 is designed/produced by designing/producing the compressor 38 basedon the reference compressor 15 so that the compressor flow rate of thecompressor 38 decreases from that of the reference compressor 15 by theincrement in the turbine flow rate, while implementing the othercomponents by reusing those of the reference model 100.

3-1. Reference Compressor

FIG. 3 is a schematic diagram showing the overall configuration of aconfiguration example of the reference compressor. FIG. 4 is across-sectional view taken in the arrow direction of the line IV-IV inFIG. 3.

As shown in FIG. 3, the reference compressor 15 includes a casing 1,disks 2 a-2 f, rotor blades 3 a-3 f, and stator blades 4 a-4 f.

The casing 1 is a cylindrical member forming a peripheral wall of thereference compressor 15. The disks 2 a-2 f, the rotor blades 3 a-3 f andthe stator blades 4 a-4 f are accommodated in the casing 1.

The disks 2 a-2 f are arranged as a stack in the flow direction of theair 19 and fastened integrally by using tie bolts 13. The disks 2 a-2 f,together with the rotor blades 3 a-3 f, constitute a rotor. As shown inFIG. 4, eight tie bolts 13 are arranged at even intervals on onecircumference centering at the central axis 11 of the referencecompressor 15. Incidentally, while a reference compressor having sixdisks 2 a-2 f is shown in FIG. 3 as an example, a compressor havingseven disks or more or five disks or less can also be employed as thereference compressor. Further, the number of the tie bolts can also bemore than or less than eight.

An annular compressor channel 32 is formed between the casing 1 and thedisks 2 a-2 f. An outer circumferential wall of the compressor channel32 is formed by an inner circumferential surface 7 of the casing 1. Aninner circumferential wall of the compressor channel 32 is formed by anouter circumferential surface 8 a of an inner circumferential member 8(explained later) and outer circumferential surfaces 6 a-6 f of thedisks 2 a-2 f. The air 19 taken into the reference compressor 15 iscompressed in the process of flowing through the compressor channel 32.The compression process of the air 19 will be explained later.

As shown in FIGS. 3 and 4, a plurality of vanes of each rotor blade 3a-3 f are arranged on the outer circumferential surface (6 a-6 f) ofeach disk 2 a-2 f at even intervals in the circumferential direction ofthe rotor. The rotor blades 3 a-3 f extend from the outercircumferential surfaces 6 a-6 f of the disks 2 a-2 f toward the outercircumferential side of the reference compressor 15 (i.e., the innercircumferential surface 7 of the casing 1). The rotor blades 3 a-3 frotate around the central axis 11 clockwise as viewed from thedownstream side (in the direction of the arrow 14 in FIG. 4) togetherwith the disks 2 a-2 f due to the air 19 flowing downstream through thecompressor channel 32.

A plurality of vanes of each stator blade 4 a-4 f are arranged on theinner circumferential surface 7 of the casing 1 at even intervals in thecircumferential direction of the rotor. The stator blades 4 a-4 f extendfrom the inner circumferential surface 7 of the casing 1 toward theinner circumferential side of the reference compressor 15 (i.e., theouter circumferential surfaces 6 a-6 f of the disks 2 a-2 f).

As shown in FIG. 3, the rotor blades 3 a-3 f and the stator blades 4 a-4f are arranged alternately in the flow direction of the air 19.Specifically, the rotor blades and the stator blades are arrangedalternately so that the rotor blade 3 a, the stator blade 4 a, the rotorblade 3 b, the stator blade 4 b, etc. are situated in this order fromthe inlet of the compressor channel 32 toward the downstream side. Apair of rotor blade and stator blade adjoining in the flow direction ofthe air 19 from the inlet of the compressor channel 32 constitutes ablade stage. In the configuration illustrated in FIG. 3, the rotor blade3 a and the stator blade 4 a constitute a first blade stage 36 a, therotor blade 3 b and the stator blade 4 b, the rotor blade 3 c and thestator blade 4 c, the rotor blade 3 d and the stator blade 4 d, and therotor blade 3 e and the stator blade 4 e respectively constitute secondthrough fifth blade stages 36 b-36 e, and the rotor blade 3 f and thestator blade 4 f constitute a sixth blade stage 36 f. In the followingdescription, the first blade stage 36 a may also be referred to as aninitial stage, the second through fifth blade stages 36 b-36 e on thedownstream side of the initial stage may also be referred to asintermediate stages, and the sixth blade stage 36 f on the downstreamside of the intermediate stages may also be referred to as a finalstage.

At a position on the upstream side of the rotor blade 3 a, the disk 2 ais supported by the inner circumferential member 8 via a shaft bearing9.

On the upstream side of the rotor blade 3 a of the initial stage 36 a, aplurality of inlet guide vanes 5 are arranged at even intervals in thecircumferential direction of the rotor. The inlet guide vanes 5 extendfrom the outer circumferential surface 8 a of the inner circumferentialmember 8 toward the inner circumferential surface 7 of the casing 1.

The compression process of the air 19 flowing downstream through thecompressor channel 32 will be explained below.

FIG. 5 is a schematic diagram illustrating the flow of the air 19flowing downstream through the compressor channel 32. FIG. 5 shows apart from the inlet guide vanes 5 to the first blade stage 36 aconstituted of the rotor blade 3 a and the stator blade 4 a. In FIG. 5,the inlet guide vanes 5 and the stator blade 4 a are stationary withrespect to the compressor channel 32, while the rotor blade 3 a isrotating with respect to the compressor channel 32 around the centralaxis 11 (see FIGS. 3 and 4) in the rotational direction indicated by thevector U.

The air 19 flowing into the inlet guide vanes 5 in the directionindicated by the vector C0 turns into the direction indicated by thevector C1 along the shape of the inlet guide vanes 5 and then flows outfrom the inlet guide vanes 5.

The air 19 flowing out from the inlet guide vanes 5 in the directionindicated by the vector C1 flows into the rotor blade 3 a situated onthe downstream side. Since the rotor blade 3 a is rotating in thedirection indicated by the vector U, the air 19 traveling in thedirection indicated by the vector C1 appears to be traveling in thedirection indicated by the vector W1 as viewed from the rotor blade 3 a.The air 19 flowing into the rotor blade 3 a apparently in the directionindicated by the vector W1 turns into the direction indicated by thevector W2 and then flows out from the rotor blade 3 a. In this case, theair 19 is decelerated from the velocity at the time of flowing into therotor blade 3 a and then flows out from the rotor blade 3 a in acompressed state. When the flow of the air 19 from the upstream side ofthe rotor blade 3 a to the downstream side of the rotor blade 3 a isviewed in the static system, the air 19 flowing into the rotor blade 3 ain the direction indicated by the vector C1 is provided with a swirlcomponent, turns into the direction indicated by the vector C2, andflows out from the rotor blade 3 a.

In the air 19 which flowed out from the rotor blade 3 a in the directionindicated by the vector C2, the swirl component provided by the rotorblade 3 a is suppressed by the stator blade 4 a situated on thedownstream side. Accordingly, the air 19 turns into the directionindicated by the vector C3 along the shape of the stator blade 4 a andthen flows out from the stator blade 4 a. In this case, the air 19 isdecelerated from the velocity at the time of flowing into the statorblade 4 a and then flows out from the stator blade 4 a in a morecompressed state. Thereafter, the air 19 is successively compressed byrepetition of the provision of the swirl component by a rotor blade andthe deprivation of the swirl component by a stator blade.

3-2. Design/Production of Compressor

FIG. 6 is a flow chart showing a design/production procedure of thecompressor 38. The design/production procedure of the compressor 38 willbe described below.

Step S1

The compressor flow rate and the compression ratio required of thecompressor 38 are determined based on the specifications of the humidair gas turbine 200.

Step S2

The annulus area of each stage from the initial stage to the final stageand the number of stages required of the compressor 38 are determinedbased on the compressor flow rate and the compression ratio determinedin the step S1. A method for determining the annulus area of each stageof the compressor 38 will be explained below.

In a compressor, a relationship indicated by the following expression(1) generally holds among the annulus area A, the compression flow ratem, the density ρ of the fluid, and the axial velocity C of the fluid:m=ρCA  (1)

In cases where the air bleeding (air extraction) or the like is notperformed on the compressor, the compression flow rate m becomes equalamong all the blade stages. The axial velocity C is also assumed to beconstant in all the blade stages in many cases. Therefore, the annulusarea A of each stage is determined according to the density ρ of thefluid to satisfy the expression (1). Since the fluid is compressed inthe process of flowing downstream through the compressor channel asmentioned above, the density ρ gradually increases and the annulus areaA gradually decreases as it goes toward the downstream side.

Assuming that internal flow conditions of the compressor 38 (i.e.,conditions such as the inflow direction of the air 19 in FIG. 5 and therevolution speed of the rotor blade 3 a) are equivalent to those of thereference compressor 15, the density ρ and the axial velocity C in theexpression (1) become equal between the reference compressor 15 and thecompressor 38, and thus the compression flow rate m and the annulus areaA of the reference compressor 15 and the compression flow rate m and theannulus area A of the compressor 38 satisfy proportionality relation.Therefore, it is sufficient if the annulus area of the compressor 38 isdetermined so that the decrease ratio of the annulus area of thecompressor 38 with respect to the reference compressor 15 becomesequivalent to the decrease ratio of the compressor flow rate of thecompressor 38 with respect to the reference compressor 15.

Step S3

Subsequently, the reference model 100 is selected based on the annulusareas and the number of stages determined in the step S2. For example, amodel including a reference compressor having annulus areas not lessthan the annulus areas determined in the step S2 and having a certainnumber of stages close to the number of stages determined in the step S2may be selected as the reference model 100. As to the annulus areas inthe reference model 100, it is desirable that the annulus area in eachstage be not less than the value (annulus area) determined in the stepS2 and the difference from the annulus area determined in the step S2 beas small as possible, for example. This is because there are contractionmargins of the annulus areas and high commonality with the compressor 38can be expected.

Step S4

Subsequently, inner radius increments and outer radius decrements of thecompressor channel 32 of the compressor 38 with respect to the referencecompressor 15 of the reference model 100 selected in the step S3 aredetermined so that the annulus areas of the compressor 38 become equalto the annulus areas determined in the step S2.

A method for decreasing the annulus areas of the reference compressor 15will be explained below.

In this embodiment, the outer radii of the compressor channel 32 aredecreased while increasing the inner radii of the compressor channel 32as shown in FIG. 3. In the following explanation, the inner radii d1-d6and the outer radii D1-D6 of the compressor channel 32 of the referencecompressor 15 will be referred to as reference inner radii and referenceouter radii, respectively. Increments in the inner radii of thecompressor channel of the compressor 38 with respect to the referenceinner radii d1-d6 will be referred to as the inner radius increments.Decrements in the outer radii of the compressor channel of thecompressor 38 with respect to the reference outer radii D1-D6 will bereferred to as the outer radius decrements.

In this embodiment, under the condition that the annulus area of eachstage of the compressor 38 becomes equal to the annulus area determinedin the step S2, the inner radius increments and the outer radiusdecrements of the initial stage 36 a, the intermediate stages 36 b-36 eand the final stage 36 f are determined so as to satisfy the followingrelationships:

Initial Stage

In the initial stage 36 a, the determination is made so that the innerradius increment is greater than the outer radius decrement.

Intermediate Stages

In each of the intermediate stages 36 b-36 e, the determination is madeso that the inner radius increment is not more than the inner radiusincrement of the previous stage and the outer radius decrement is notless than the outer radius decrement of the previous stage. For example,in the third blade stage 36 c, the determination is made so that theinner radius increment is not more than the inner radius increment ofthe second blade stage 36 b as the previous stage and the outer radiusdecrement is not less than the outer radius decrement of the secondblade stage 36 b as the previous stage.

Final Stage

In the final stage 36 f, the determination is made so that the outerradius decrement is not less than the inner radius increment.

Step S5

The compressor 38 is designed by updating components in the initialstage 36 a, the intermediate stages 36 b-36 e and the final stage 36 fof the reference compressor 15 (the casing 1, the disks 2 a-2 f, therotor blades 3 a-3 f, the stator blades 4 a-4 f, etc.) that deviatedfrom the specifications due to the inner radius increment and the outerradius decrement determined in the step S4 so that the updatedcomponents fulfill the specifications, while reusing components that arecommon in regard to the specifications. In this embodiment, thespecifications are requirements that the components should fulfill.

Step S6

The compressor 38 is produced according to the design in the step S5.

Incidentally, the humid air gas turbine 200 is produced by using thecompressor 38 produced in the step S6.

Effect

(1) Reduction in Compressor Flow Rate

In this embodiment, the annulus areas required of the compressor 38 aredetermined from the specifications of the humid air gas turbine 200, andthe inner radius increments and the outer radius decrements of thecompressor channel 32 of the compressor 38 with respect to the referencecompressor 15 are determined so that the annulus areas of the compressor38 become equal to the determined annulus areas. Therefore, thecompressor flow rate of the compressor 38 can be reduced with respect tothe reference compressor 15 by the increment in the turbine flow rate.

(2) Maintaining of Compressor Efficiency

Besides the above-described method, there are methods called “tip cut”and “hub up” for decreasing the annulus areas of the referencecompressor 15.

FIG. 7 is a schematic diagram for explaining the tip cut. Parts in FIG.7 equivalent to those in the reference compressor 15 in the firstembodiment are assigned the already used reference characters andrepeated explanation thereof is omitted properly.

As shown in FIG. 7, the tip cut is a method that just decreases theouter radii of the compressor channel 32 of the reference compressor 15(i.e., changes the inner circumferential surface 7 to the innercircumferential surface 7′) without increasing the inner radii of thecompressor channel 32.

FIG. 8 is a schematic diagram for explaining the hub up. Parts in FIG. 8equivalent to those in the reference compressor 15 in the firstembodiment are assigned the already used reference characters andrepeated explanation thereof is omitted properly.

As shown in FIG. 8, the hub up is a method that just increases the innerradii of the compressor channel 32 of the reference compressor 15 (i.e.,changes the outer circumferential surfaces 6 a-6 f and 8 a to the outercircumferential surfaces 6 a′-6 f′ and 8 a′) without decreasing theouter radii of the compressor channel 32.

The compressor efficiency is mainly determined by the stage load and theblade height (blade length) of each blade stage. The compressorefficiency increases with the decrease in the stage load and with theincrease in the blade height.

Compressor Efficiency and Stage Load

A stage loading factor ψ is defined as an index of the load in any givenblade stage of the compressor. The compressor efficiency increases withthe decrease in the stage loading factor ψ and decreases with theincrease in the stage loading factor ψ. The stage loading factor ψ canbe represented as the following expression (2) by using an enthalpyincrement Δh in any given blade stage and a circumferential velocity uat the average radius of the rotor blades:ψ=h/u ²  (2)

FIG. 9 is a diagram illustrating the relationship between the stageloading factor and the blade stages. The vertical axis represents thestage loading factor ψ and the horizontal axis represents the bladestages. Each number on the horizontal axis corresponds to the stagenumber of each blade stage with reference to the initial stage.Specifically, the number 1 corresponds to the initial stage, the numbers2-5 correspond to the intermediate stages, and the number 6 correspondsto the final stage (see FIG. 3). In FIG. 9, the chain line representsthe stage loading factor ψ31 of the reference compressor 15, the dottedline represents the stage loading factor ψ32 of the compressor after thetip cut, the broken line represents the stage loading factor ψ33 of thecompressor after the hub up, and the solid line represents the stageloading factor ψ34 of the compressor 38.

As shown in FIG. 9, the stage loading factor ψ33 of the compressor afterthe hub up becomes smaller than the stage loading factor ψ31 of thereference compressor 15 throughout all stages from the initial stage tothe final stage. Therefore, the compressor efficiency of the compressorafter the hub up becomes higher than that of the reference compressor15. The reason why the stage loading factor ψ33 of the compressor afterthe hub up becomes smaller than the stage loading factor ψ31 of thereference compressor 15 is that the hub up increases the average radiusof the rotor blades and thereby increases the circumferential velocityu. In this embodiment, the average radius of the blades is the distancefrom the central axis 11 to a central part of the blades. In contrast,the stage loading factor ψ32 after the tip cut becomes larger than thestage loading factor ψ31 of the reference compressor 15 throughout allstages from the initial stage to the final stage. Therefore, thecompressor efficiency of the compressor after the tip cut becomes lowerthan that of the reference compressor 15. The reason why the stageloading factor ψ32 after the tip cut becomes larger than the stageloading factor ψ31 of the reference compressor 15 is that the tip cutdecreases the average radius of the rotor blades and thereby decreasesthe circumferential velocity u. The superiority of the hub up to the tipcut in regard to the change in the stage loading factor ψ becomesincreasingly remarkable as it goes toward the initial stage. This isbecause the stage loading factor ψ changes greatly as it goes toward theinitial stage since the blade height increases and the change in theaverage radius increases as it goes toward the initial stage.

Compressor Efficiency and Blade Height

In general, with the increase in the blade height, the flow rate of partof the air 19 in the compressor channel 32 that causes friction againstthe outer circumferential surfaces 6 a-6 f and the inner circumferentialsurface 7 decreases, and consequently, the fluid loss decreases. Incontrast, decreasing the annulus area leads to a decrease in the bladeheight, and thus the flow rate of part of the air 19 in the compressorchannel 32 that causes friction against the outer circumferentialsurfaces 6 a-6 f and the inner circumferential surface 7 increases, andconsequently, the fluid loss caused by the outer circumferentialsurfaces 6 a-6 f and the inner circumferential surface 7 increases.Further, vortices develop in the compressor channel 32 due to thefriction occurring between the air 19 and the outer circumferentialsurfaces 6 a-6 f and the inner circumferential surface 7, and thevortices interfere with the air 19. Consequently, the compressorefficiency decreases.

FIG. 10 is a diagram illustrating the relationship between a bladeheight decrease ratio and the blade stages. The vertical axis representsthe blade height decrease ratio and the horizontal axis represents theblade stages. The numbers on the horizontal axis are the same as thosein FIG. 9. In FIG. 10, the dotted line represents the blade heightdecrease ratio 35 of the compressor after the tip cut, the broken linerepresents the blade height decrease ratio 36 of the compressor afterthe hub up, and the solid line represents the blade height decreaseratio 37 of the compressor 38. In this embodiment, the blade heightdecrease ratio, in the case of the compressor 38, for example, isrepresented by a value obtained by dividing the blade height difference(in any given stage) between the reference compressor 15 and thecompressor 38 by the blade height in the reference compressor 15. Thecompressor efficiency decreases with the increase in the blade heightdecrease ratio.

As shown in FIG. 10, the blade height decrease ratio 35 of thecompressor after the tip cut becomes smaller than the blade heightdecrease ratio 36 after the hub up throughout all stages from theinitial stage to the final stage. Therefore, the hub up is capable ofrestraining the deterioration in the compressor efficiency with respectto the reference compressor 15 better than the tip cut. Further, thedifference between the blade height decrease ratio 36 after the hub upand the blade height decrease ratio 35 after the tip cut increases as itgoes toward rear stages where the blade height is originally small.Thus, the hub up is capable of better restraining the deterioration inthe compressor efficiency than the tip cut more remarkably on the rearstages side.

In this embodiment, the outer radii are decreased in the rear stageswhile increasing the inner radii in the front stages by making thedetermination in the initial stage so that the inner radius increment isgreater than the outer radius decrement, making the determination ineach of the intermediate stages so that the inner radius increment isnot more than the inner radius increment of the previous stage and theouter radius decrement is not less than the outer radius decrement ofthe previous stage, and making the determination in the final stage sothat the outer radius decrement is not less than the inner radiusincrement. Therefore, as shown in FIGS. 9 and 10, in the front stages,the stage loading factor ψ34 can be made small and the blade heightdecrease ratio 37 can be made smaller than in the rear stages similarlyto the case of the hub up. Thus, a compressor efficiency improvementeffect that is achieved by making the stage loading factor ψ34 smallbecomes dominant in the front stages. In the rear stages, the bladeheight decrease ratio 37 can be made small and the stage loading factorψ34 can be made smaller than in the front stages similarly to the caseof the tip cut. Thus, a compressor efficiency improvement effect that isachieved by making the blade height decrease ratio small becomesdominant in the rear stages.

FIG. 11 is a diagram illustrating the compression ratio dependence ofthe compressor efficiency. The vertical axis represents the compressorefficiency and the horizontal axis represents the compression ratio. InFIG. 11, the dotted line represents the case of the tip cut, the brokenline represents the case of the hub up, and the solid line representsthe case of this embodiment.

In general, the compressor efficiency is designed so as to hit themaximum at a compression ratio at the design point. Since thisembodiment employs a configuration advantageous in terms of thecompressor efficiency both in the front stages and in the rear stages asmentioned above, this embodiment is capable of maintaining highercompressor efficiency in the entire compressor compared to theconfigurations simply employing the tip cut or the hub up as shown inFIG. 11.

(3) Securement of Reliability

In this embodiment, among the components of the reference compressor 15having past records of design or production, those fulfilling thespecifications required of the compressor 38 can be reused (i.e.,diverted from the reference compressor 15 to the compressor 38).Therefore, in regard to such components diverted from the referencecompressor 15, the reliability can be secured without the need ofspecially conducting verification or the like.

(4) Increase in Natural Frequency

In general, the natural frequency of the rotor can be increased byincreasing the shaft diameter of the rotor. However, in theconfiguration illustrated in FIG. 3, increasing the shaft diameter ofthe rotor can lead to interference with the inner circumferential member8.

In contrast, in this embodiment, along with the increase in the innerradii in the front stages, the outer circumferential surface 8 a of theinner circumferential member 8 is raised in the radial direction, andthus the thickness (width in the radial direction) of the innercircumferential member 8 increases. Therefore, the bottom surface of theinner circumferential member 8 (surface facing the disk 2 a) can beraised in the radial direction by a distance equal to the increment inthe thickness. Accordingly, the natural frequency of the rotor can beincreased by increasing the shaft diameter d7 of the rotor to d7′without causing the interference with the inner circumferential member8. Consequently, the possibility of the occurrence of the rotorvibration problem decreases and the reliability of the compressor can beincreased.

Second Embodiment

Configuration

FIG. 12 is a schematic diagram showing the overall configuration of aconfiguration example of a reference compressor according to a secondembodiment of the present invention. Parts in FIG. 12 equivalent tothose in the reference compressor 15 in the first embodiment areassigned the already used reference characters and repeated explanationthereof is omitted properly.

As shown in FIG. 12, the reference compressor 115 according to thisembodiment differs from the reference compressor 15 in that thereference compressor 115 includes outer radius constant stages (aninitial stage 136 a and an intermediate stage 136 b in FIG. 12) in whichthe reference outer radius is constant from the initial stage 136 atoward the downstream side and an outer radius decreasing stage (anintermediate stage 136 c in FIG. 12) which connects to the downstreamside of the outer radius constant stages 136 a and 136 b and in whichthe reference outer radius decreases toward the downstream side. Therest of the configuration is equivalent to that in the referencecompressor 15.

In this embodiment, the inner radius increments and the outer radiusdecrements in the outer radius constant stages 136 a and 136 b and theouter radius decreasing stage 136 c of the reference compressor 115 aredetermined by adding conditions to the step S4 in the first embodiment.The other steps are equivalent to those in the first embodiment.

In this embodiment, the inner radius increments and the outer radiusdecrements in the outer radius constant stages 136 a and 136 b and theouter radius decreasing stage 136 c are determined so as to satisfy thefollowing relationships:

Outer Radius Constant Stages

In the outer radius constant stages 136 a and 136 b, the innercircumferential surface 7 is changed to the inner circumferentialsurface 7″ by uniformly decreasing the reference outer radii D1 and D2so that D1 and D2 become equal to the outer radius at a downstream endstage in the outer radius constant stages 136 a and 136 b in a casewhere only the reference outer radii D1 and D2 are decreased, while thereference inner radii d1 and d2 are increased according to the decrementin the reference outer radii D1 and D2 (i.e., so as to compensate forthe decrease in the decrements in the annulus areas in the outer radiusconstant stages 136 a and 136 b caused by the uniform decreasing of thereference outer radii D1 and D2).

Outer Radius Decreasing Stage

In the outer radius decreasing stage 136 c, the reference outer radiusD3 is decreased so that decrements in the annulus areas of the referencecompressor 115 with respect to the determined annulus areas becomeuniform.

Incidentally, while a case where only the tip cut is conducted in theouter radius decreasing stage 136 c is illustrated in FIG. 12, it isalso possible to conduct the hub up in addition to the tip cut whennecessary.

Effect

With the above-described configuration, this embodiment achieves thefollowing effect in addition to the aforementioned effects achieved inthe first embodiment.

When the annulus areas of the reference compressor 115 are decreased bymeans of the tip cut, there are cases where the outer radius increasesas it goes downstream in the outer radius constant stages 136 a and 136b (i.e., the inner circumferential surface 7 becomes like the innercircumferential surface 7′″). In cases where the thrust load is borne bythe shaft bearing 9, along with the thermal extension due to the gasturbine operation, the disks 2 a-2 f and the rotor blades 3 a-3 f movedownstream (rightward in FIG. 12) with reference to the shaft bearing 9.Then, the clearance between the inner circumferential surface 7′″ andthe rotor blades 3 a-3 b enlarges and that can lead to a drop in thecompressor efficiency.

In contrast, in this embodiment, the reference outer radii D1 and D2 aredecreased uniformly in the outer radius constant stages 136 a and 136 b.Thus, even when the disks 2 a-2 f and the rotor blades 3 a-3 f movedownstream, the clearance between the inner circumferential surface 7″and the rotor blades 3 a-3 b does not enlarge and the drop in thecompressor efficiency can be inhibited.

Third Embodiment

Configuration

FIG. 13 is a schematic diagram showing the overall configuration of aconfiguration example of a compressor according to a third embodiment ofthe present invention. Parts in FIG. 13 equivalent to those in thereference compressor 15 in the first embodiment are assigned the alreadyused reference characters and repeated explanation thereof is omittedproperly.

As shown in FIG. 13, this embodiment differs from the first embodimentin that a blade stage 36 g including a disk 2 g, a stator blade 4 g anda rotor blade 3 g is added to the downstream side of the final stage 36f of the compressor designed/produced based on the reference compressor15. The rest of the configuration is equivalent to that in the firstembodiment.

Effect

With the above-described configuration, this embodiment achieves thefollowing effect in addition to the aforementioned effects achieved inthe first embodiment.

When it is desirable to also change the compression ratio in addition tothe reduction in the compressor flow rate, the purpose can be achievedby decreasing the compressor flow rate and then changing the number ofblade stages. For example, the compression ratio can be raised by addingthe blade stage 36 g to the downstream side of the final stage 36 f asin this embodiment. Incidentally, the compression ratio can be raisedfurther by increasing the number of blade stages added. Conversely, itis also possible to lower the compression ratio by decreasing the numberof blade stages.

Fourth Embodiment

Configuration

FIG. 14 is a schematic diagram showing a configuration example of inletguide vanes according to a fourth embodiment of the present invention.

This embodiment differs from the reference compressor 15 in that theinlet guide vanes 5 are replaced with inlet guide vanes 205 (205A, 205B,etc.) shown in FIG. 14 each of which is rotatable around a shaft 42 as arotary shaft extending in the blade length direction. The rest of theconfiguration is equivalent to that in the reference compressor 15.

The compressor flow rate is determined in proportion to the size of athroat 40. The throat 40 means the length of a line connecting aposition on a vane back surface 205 a of the inlet guide vane 205A and aposition on a vane back surface 205 b of the inlet guide vane 205B(adjoining the inlet guide vane 205A in the circumferential direction ofthe rotor) that minimize the distance between the vane back surfaces 205a and 205 b. As shown in FIG. 14, by rotating the inlet guide vanes 205around the rotary shafts 42 clockwise (in the direction of the arrow 43in FIG. 14) into the inlet guide vanes 205′ (205A′, 205B′, etc.), thethroat 40 is changed to the throat 40′. Since the throat 40′ is shorterthan the throat 40, the compressor flow rate decreases. Conversely, ifthe inlet guide vanes 205 are rotated counterclockwise, the throat 40becomes longer and thus the compressor flow rate increases. To sum up,the inlet guide vanes 205 have a compressor flow rate regulationfunction.

Effect

With the above-descried configuration, this embodiment achieves thefollowing effect in addition to the aforementioned effects achieved inthe first embodiment.

In the first embodiment, greatly decreasing the annulus areas can leadto excessively low blade heights in blade stages on the downstream side,and consequently, to a significant drop in the compressor efficiency.

In this embodiment, in addition to the method of reducing the compressorflow rate by decreasing the annulus areas, it is also possible to reducethe compressor flow rate by rotating the inlet guide vanes 205. Thus,even when greatly decreasing the annulus areas is necessary, it ispossible to rotate the inlet guide vanes 205, thereby reduce thecompressor flow rate, and correspondingly reduce the decrease in theannulus areas. Accordingly, it is possible to inhibit a great decreasein the annulus areas and thereby avoid the excessively low blade heightsand the significant drop in the compressor efficiency.

While a case where the rotatable inlet guide vanes 205 are providedinstead of the inlet guide vanes 5 has been illustrated in thisembodiment, it is also possible to reuse the inlet guide vanes 5 if theinlet guide vanes 5 have originally been configured to be rotatable. Theabove-descried effect can be achieved also in this case.

Other Examples

The present invention is not restricted to the above-descriedembodiments but includes a variety of modifications. For example, theabove embodiments, which have been described in detail for the purposeof easily understandable description of the present invention, are notnecessarily restricted to those including the whole of the describedconfiguration. For example, it is possible to replace part of theconfiguration of an embodiment with a configuration in anotherembodiment, or to delete part of the configuration of each embodiment.

In the above embodiments, cases where the inner radius increment isdetermined to be greater than the outer radius decrement in the initialstage 36 a have been described as examples. However, the essentialeffect of the present invention is to provide design and productionmethods of a gas turbine capable of reducing the compressor flow rate incomparison with the reference model while maintaining a compressionratio equivalent to that in the reference model, and thus the presentinvention is not restricted to such cases as long as the essentialeffect is achieved. For example, the inner radius increment may also bedetermined to be equal to the outer radius decrement or less than theouter radius decrement in the initial stage 36 a.

Further, while the casing 1 is formed of one sheet-like member in theabove-descried embodiments, the present invention is not restricted tosuch a configuration as long as the aforementioned essential effect ofthe present invention is achieved. For example, the casing 1 may also beformed by stacking a plurality of cylindrical separate members.

Furthermore, while examples of applying the present invention to a humidair gas turbine 200 have been described in the above embodiments, thepresent invention is widely applicable to gas turbines that employ thecycle of injecting steam into the combustor. The present invention isapplicable also to blast furnace gas firing gas turbines and the like.

DESCRIPTION OF REFERENCE CHARACTERS

-   15, 115: Reference compressor-   100: Reference gas turbine-   200: Derivative gas turbine-   32: Compressor channel-   d1-d6: Reference inner radius-   D1-D6: Reference outer radius-   38: Compressor-   36 a, 136 a: Initial stage-   36 b-36 e: Intermediate stage-   36 f, 136 f: Final stage-   5, 205: Inlet guide vane

What is claimed is:
 1. A gas turbine production method for producing aderivative gas turbine of a different cycle based on a reference gasturbine including a reference compressor, wherein: letting a referenceinner radius and a reference outer radius respectively represent aninner radius and an outer radius of an annular compressor channel of thereference compressor, an inner radius increment represent an incrementin an inner radius of a compressor channel of the derivative gas turbinewith respect to the reference inner radius, and an outer radiusdecrement represent a decrement in an outer radius of the compressorchannel of the derivative gas turbine with respect to the referenceouter radius, the gas turbine production method comprising the steps of:determining a compressor flow rate and a compression ratio required of acompressor of the derivative gas turbine; determining annulus areasrequired of the compressor of the derivative gas turbine based on thedetermined compressor flow rate and compression ratio; determining theinner radius increment and the outer radius decrement of an initialstage, determining the inner radius increment and the outer radiusdecrement of each of intermediate stages on the downstream side of theinitial stage such that the inner radius increment is not more than theinner radius increment of the previous stage and the outer radiusdecrement is not less than the outer radius decrement of the previousstage, and determining the inner radius increment and the outer radiusdecrement of a final stage on the downstream side of the intermediatestages such that the outer radius decrement is not less than the innerradius increment under a condition that the outer radius of thecompressor channel is decreased, the inner radius of the compressorchannel is increased, and the annulus area of each stage of thecompressor of the derivative gas turbine becomes equal to the determinedannulus area; designing the compressor of the derivative gas turbine byupdating design data of components of the reference compressor thatdeviated from specifications due to the determination of the innerradius increment and the outer radius decrement such that the updateddesign data fulfill the specifications in the initial stage, in each ofthe intermediate stages, and in the final stage; and producing thecompressor of the derivative gas turbine based on the design and therebyproducing the derivative gas turbine.
 2. The gas turbine productionmethod according to claim 1, wherein the inner radius increment isdetermined to be greater than the outer radius decrement in the initialstage.
 3. The gas turbine production method according to claim 1,wherein decrements in the annulus areas of the reference compressor withrespect to the determined annulus areas are made uniform.
 4. The gasturbine production method according to claim 1, wherein in each stage onthe downstream side of the initial stage, a decrement in the annulusarea of the reference compressor with respect to the determined annulusarea is made greater than the decrement in the previous stage.
 5. Thegas turbine production method according to claim 1, wherein: thereference compressor includes outer radius constant stages in which thereference outer radius is constant from the initial stage toward thedownstream side and an outer radius decreasing stage that connects tothe outer radius constant stages and in which the reference outer radiusdecreases toward the downstream side, in the outer radius constantstages, the annulus area in each stage is made equal to the determinedannulus area by uniformly decreasing the reference outer radii in thestages such that the reference outer radii become equal to the outerradius at a downstream end stage in the outer radius constant stages ina case where only the reference outer radii are decreased, whileincreasing the reference inner radii according to the decrement in thereference outer radii, and in the outer radius decreasing stage, thereference outer radius is decreased such that decrements in the annulusareas of the reference compressor with respect to the determined annulusareas become uniform.
 6. The gas turbine production method according toclaim 1, wherein at least one stage is added to the downstream side ofthe final stage.
 7. The gas turbine production method according to claim1, wherein inlet guide vanes each of which rotates around a shaftextending in a blade length direction as a rotary shaft are provided onthe upstream side of the initial stage.
 8. A gas turbine design methodfor designing a derivative gas turbine of a different cycle based on areference gas turbine including a reference compressor, wherein: lettinga reference inner radius and a reference outer radius respectivelyrepresent an inner radius and an outer radius of an annular compressorchannel of the reference compressor, an inner radius increment representan increment in an inner radius of a compressor channel of thederivative gas turbine with respect to the reference inner radius, andan outer radius decrement represent a decrement in an outer radius ofthe compressor channel of the derivative gas turbine with respect to thereference outer radius, the gas turbine design method comprising thesteps of: determining a compressor flow rate and a compression ratiorequired of a compressor of the derivative gas turbine; determiningannulus areas required of the compressor of the derivative gas turbinebased on the determined compressor flow rate and compression ratio;determining the inner radius increment and the outer radius decrement ofan initial stage, determining the inner radius increment and the outerradius decrement of each of intermediate stages on the downstream sideof the initial stage such that the inner radius increment is not morethan the inner radius increment of the previous stage and the outerradius decrement is not less than the outer radius decrement of theprevious stage, and determining the inner radius increment and the outerradius decrement of a final stage on the downstream side of theintermediate stages such that the outer radius decrement is not lessthan the inner radius increment under a condition that the outer radiusof the compressor channel is decreased, the inner radius of thecompressor channel is increased, and the annulus area of each stage ofthe compressor of the derivative gas turbine becomes equal to thedetermined annulus area; and designing the compressor of the derivativegas turbine by updating design data of components of the referencecompressor that deviated from specifications due to the determination ofthe inner radius increment and the outer radius decrement such that theupdated design data fulfill the specifications in the initial stage, ineach of the intermediate stages, and in the final stage, and therebydesigning the derivative gas turbine.
 9. A gas turbine production methodfor producing a derivative gas turbine of a different cycle based on areference gas turbine including a reference compressor, wherein: lettinga reference inner radius and a reference outer radius respectivelyrepresent an inner radius and an outer radius of an annular compressorchannel of the reference compressor, an inner radius increment representan increment in an inner radius of a compressor channel of thederivative gas turbine with respect to the reference inner radius, andan outer radius decrement represent a decrement in an outer radius ofthe compressor channel of the derivative gas turbine with respect to thereference outer radius, the gas turbine production method comprising thesteps of: determining a compressor flow rate and a compression ratiorequired of a compressor of the derivative gas turbine; determiningannulus areas required of the compressor of the derivative gas turbinebased on the determined compressor flow rate and compression ratio;determining the inner radius increment and the outer radius decrement ofan initial stage, determining the inner radius increment and the outerradius decrement of each of intermediate stages on the downstream sideof the initial stage such that the inner radius increment is not morethan the inner radius increment of the previous stage and the outerradius decrement is not less than the outer radius decrement of theprevious stage, and determining the inner radius increment and the outerradius decrement of a final stage on the downstream side of theintermediate stages such that the outer radius decrement is not lessthan the inner radius increment under a condition that the annulus areaof each stage of the compressor of the derivative gas turbine becomesequal to the determined annulus area; designing the compressor of thederivative gas turbine by updating design data of components of thereference compressor that deviated from specifications due to thedetermination of the inner radius increment and the outer radiusdecrement such that the updated design data fulfill the specificationsin the initial stage, in each of the intermediate stages, and in thefinal stage; and producing the compressor of the derivative gas turbinebased on the design and thereby producing the derivative gas turbine,wherein: the reference compressor includes outer radius constant stagesin which the reference outer radius is constant from the initial stagetoward the downstream side and an outer radius decreasing stage thatconnects to the outer radius constant stages and in which the referenceouter radius decreases toward the downstream side, in the outer radiusconstant stages, the annulus area in each stage is made equal to thedetermined annulus area by uniformly decreasing the reference outerradii in the stages such that the reference outer radii become equal tothe outer radius at a downstream end stage in the outer radius constantstages in a case where only the reference outer radii are decreased,while increasing the reference inner radii according to the decrement inthe reference outer radii, and in the outer radius decreasing stage, thereference outer radius is decreased such that decrements in the annulusareas of the reference compressor with respect to the determined annulusareas become uniform.